摘要翻译：
考虑同时测试$S$假设的问题。通常的方法将注意力限制在控制哪怕一次错误拒绝概率的程序上，即家庭错误率(FWER)。如果$S$很大，则可能愿意容忍多个错误拒绝，从而增加过程正确拒绝错误空假设的能力。一种可能是通过控制$K$或更多的错误拒绝的概率来取代对FWER的控制，这被称为$K$-FWER。根据具体情况，我们导出了单步和降压过程来控制有限样本中的$k$-fwer或渐近控制$k$-fwer。我们还考虑错误发现比例(FDP)定义为错误拒绝的数量除以拒绝的总数（如果没有拒绝，定义为0）。Benjamini和Hochberg提出的错误发现率[J.Roy.Statist.Soc.Ser.B57(1995)289--300]控制着$E(FDP)$.这里的目标是构造方法，对于给定的$\gamma$和$\alpha$，$p\{fdp>\gamma\}\le\alpha$至少是渐近地满足的。与Lehmann和Romano[Ann.statist.33(2005)1138-1154]的建议不同，我们构造了隐式考虑单个检验统计量的依赖结构的方法，以进一步提高检测假空假设的能力。van der Laan、Dudoit和Pollard的相关工作也具有这一特点[Stat.appl.Genet.Mol.Biol.3(2004)第15条]，但我们的研究方法有很大不同。像Pollard和van der Laan的工作[Proc.2003国际计算机科学与工程多会议，METMBS'03会议(2003)3-9]和Dudoit,van der Laan和Pollard[Stat.Appl.Genet.Mol.Biol.3(2004)第13条]一样，我们使用重采样方法来实现我们的目标。一些模拟将有限样本的性能与目前可用的方法进行了比较。
---
英文标题：
《Control of generalized error rates in multiple testing》
---
作者：
Joseph P. Romano, Michael Wolf
---
最新提交年份：
2007
---
分类信息：

一级分类：Mathematics        数学
二级分类：Statistics Theory        统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
--
一级分类：Statistics        统计学
二级分类：Statistics Theory        统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
--

---
英文摘要：
  Consider the problem of testing $s$ hypotheses simultaneously. The usual approach restricts attention to procedures that control the probability of even one false rejection, the familywise error rate (FWER). If $s$ is large, one might be willing to tolerate more than one false rejection, thereby increasing the ability of the procedure to correctly reject false null hypotheses. One possibility is to replace control of the FWER by control of the probability of $k$ or more false rejections, which is called the $k$-FWER. We derive both single-step and step-down procedures that control the $k$-FWER in finite samples or asymptotically, depending on the situation. We also consider the false discovery proportion (FDP) defined as the number of false rejections divided by the total number of rejections (and defined to be 0 if there are no rejections). The false discovery rate proposed by Benjamini and Hochberg [J. Roy. Statist. Soc. Ser. B 57 (1995) 289--300] controls $E(FDP)$. Here, the goal is to construct methods which satisfy, for a given $\gamma$ and $\alpha$, $P\{FDP>\gamma\}\le \alpha$, at least asymptotically. In contrast to the proposals of Lehmann and Romano [Ann. Statist. 33 (2005) 1138--1154], we construct methods that implicitly take into account the dependence structure of the individual test statistics in order to further increase the ability to detect false null hypotheses. This feature is also shared by related work of van der Laan, Dudoit and Pollard [Stat. Appl. Genet. Mol. Biol. 3 (2004) article 15], but our methodology is quite different. Like the work of Pollard and van der Laan [Proc. 2003 International Multi-Conference in Computer Science and Engineering, METMBS'03 Conference (2003) 3--9] and Dudoit, van der Laan and Pollard [Stat. Appl. Genet. Mol. Biol. 3 (2004) article 13], we employ resampling methods to achieve our goals. Some simulations compare finite sample performance to currently available methods.
---
PDF链接：
https://arxiv.org/pdf/710.2258